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Multifractal and low-dimensional representations of high-frequency return distribution sequences

Chun-Xiao Nie

The Journal of Finance and Data Science2025https://doi.org/10.1016/j.jfds.2025.100173article
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0.50

What the paper says

High-frequency returns are of great significance to financial risk management and investment. This study analyzes the dynamics of the high-frequency return distributions. The calculations show that the high-frequency return distribution sequence has a small intrinsic dimension and exhibits time-varying characteristics. We find that all subdistribution sequences included multifractal structures, and the global Rényi index ( GRI ) series showed that the multifractal features changed over time. We also constructed a benchmark distribution sequence, in which each distribution was sampled from a normal population and the mean and standard deviation of the original series were maintained. The calculations show that the benchmark sequence also includes multifractal features, and the correlation dimension and GRI are smaller than those of the original sequence. However, the calculations show that there is a high correlation between the dimensional series of the benchmark sequence and the original sequence, suggesting that the mean and standard deviation are important parameters affecting fractal dynamics. In particular, we use the UMAP algorithm to show the low-dimensional representation of the distribution sequence, and find that the small-dimensional subsequences include earthworm-like clusters, while the subsequences with large-dimensions include cloud-like clusters. This study provides a new way to analyze the distribution of high-frequency returns, and explores the characteristics of distribution sequences, which is helpful for understanding the dynamics of distributions.

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https://doi.org/https://doi.org/10.1016/j.jfds.2025.100173

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@article{chun-xiao2025,
  title        = {{Multifractal and low-dimensional representations of high-frequency return distribution sequences}},
  author       = {Chun-Xiao Nie},
  journal      = {The Journal of Finance and Data Science},
  year         = {2025},
  doi          = {https://doi.org/https://doi.org/10.1016/j.jfds.2025.100173},
}

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Multifractal and low-dimensional representations of high-frequency return distribution sequences

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0.50

Balanced mode · F 0.40 / M 0.15 / V 0.05 / R 0.40

F · citation impact0.50 × 0.4 = 0.20
M · momentum0.50 × 0.15 = 0.07
V · venue signal0.50 × 0.05 = 0.03
R · text relevance †0.50 × 0.4 = 0.20

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